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Archimedes: Archimedes System
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The end of Archimedes life was anything but uneventful. King Hiero had been so impressed with his friend's inventions that he persuaded him to develop weapons to defend the city. These inventions would prove quite useful. In 212 B.C., Marcellus, a Roman general, decided to conquer Syracuse with a full frontal assault on both land and sea. The Roman legions were routed. Huge catapults hurled 500 pound boulders at the soldiers; large cranes with claws on the end lowered down on the enemy ships, lifted them in the air, and then threw them against the rocks; and systems of mirrors focused the sun rays to light enemy ships on fire.
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In The Sand Reckoner, Archimedes set out to calculate the number of grains of sand that the universe could contain. In doing so, he challenged the notion that the number of grains of sand was too large to be counted. He wrote: "There are some, King Gelo (Gelo II, son of Hiero II), who think that the number of the sand is infinite in multitude; and I mean by the sand not only that which exists about Syracuse and the rest of Sicily but ... that which is found in every region whether inhabited or uninhabited." To solve the problem, Archimedes devised a system of counting based around the myriad. The word is based on the Greek for uncountable, murious, and was also used to denote the number 10,000. He proposed a number system using powers of myriad myriads (100 million) and concluded that the number of grains of sand required to fill the universe would be 8 × 1063, which can also be expressed as eight vigintillions.
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Archimedes Systems provides commercial services through its own consulting services and non-free web hosting. Somewhat like other companies which blend their commercial services with open source offerings, Archimedes ... serves the public good by providing the means of a free web presence via Nostromo (e.g. yoursite.nostromo.com). Because there are individuals or organizational entities which feel sufficiently compelled to have a less obvious connection to Nostromo or Archimedes, Web Channel provides fee-based services for establishing and maintaining your web presence. (e.g. yoursite.com), on one of its own servers or the server of another ISP.
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Lastly, Archimedes is credited with the famous Cattle-Problem enunciated in the epigram edited by Gotthold Ephraim Lessing in 1773, which purports to have been sent by Archimedes to the mathematicians at Alexandria in a letter to Eratosthenes. Of lost works by Archimedes we can identify the following: (1) investigations on polyhedra mentioned by Pappus; (2) a book addressed to Zeuxippus and dealing with the naming of numbers on the system explained in the Sand Reckoner; (3) On balances or levers; (4) On centers of gravity; (5) an optical work from which Theon of Alexandria quotes a remark about refraction; (6) a Method, mentioned by Suïdas; (7) On Sphere-making, in which Archimedes explained the construction of the sphere which he made to imitate the motions of the sun, the moon and the five planets in the heavens. Cicero actually saw this contrivance and describes it in De Republica.
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In this treatise, Archimedes counts the number of grains of sand that will fit inside the universe. This book mentions the heliocentric theory of the solar system proposed by Aristarchus of Samos, contemporary ideas about the size of the Earth and the distance between various celestial bodies. By using a system of numbers based on powers of the myriad, Archimedes concludes that the number of grains of sand required to fill the universe is 8 × 1063 in modern notation. The introductory letter states that Archimedes' father was an astronomer named Phidias. The Sand Reckoner or Psammites is the only surviving work in which Archimedes discusses his views on astronomy.[41]
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The answer of 17152 combinations by Archimedes requires a careful, systematic counting of all possibilities. "It was hard," said Persi Diaconis, a Stanford statistician who worked on it with his wife Susan Holmes, and a second husband-and-wife team of combinatorial mathematicians, Ronald Graham and Fan Chung from the University of California, San Diego. Independently, a computer scientist, William Cutler at Chicago Rawhide wrote a program that confirmed that the mathematicians' answer was correct. The Stomachion, according to Dr. Reviel Netz, was far ahead of its time: a treatise on combinatorics, a field that did not come into its own until the rise of computer science.
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